Answer
$$i^{24}+i^{61}=i+1$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}i^{24}+i^{61}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}1+i \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}i+1\end{aligned} $$ | |
| ① | $$ i^{24} = i^{4 \cdot 6 + 0} =
\left( i^4 \right)^{ 6 } \cdot i^0 =
1^{ 6 } \cdot 1 =
1 $$ |
| ② | $$ i^{61} = i^{4 \cdot 15 + 1} =
\left( i^4 \right)^{ 15 } \cdot i^1 =
1^{ 15 } \cdot i =
i $$ |
| ③ | Combine like terms: $$ i+1 = i+1 $$ |
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